Under the perpetual inventory system, the account Purchases won't exist. Rather, the cost of inventory items purchased will be recorded directly into the account Inventory.
Under the periodic system, the cost in the account Purchases will be added to the cost of the beginning inventory to arrive at the cost of goods available. The cost of the ending inventory is computed through a physical count (or an estimate) and is subtracted from the cost of goods available. The resulting amount is the cost of goods sold.
Under the perpetual system, the balance in the account Inventory should be the cost of the ending inventory. Under the perpetual system, the cost of goods sold will have been removed from the account Inventory when the items were sold and placed in the account Cost of Goods Sold.
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